AUM Block Geometric Mean Labeling For Star Family with an Application in Coding Theory

Abstract

This paper introduces a new concept of AUM block geometric mean labeling for star, bistar and U- star graphs. AUM block geometric mean labeling, a recent development in graph theory, involves assigning labels to blocks so that the geometric mean of the labels on adjacent points and the connecting lines satisfy specific criteria. The use of AUM block geometric mean labeling in cryptography is also presented. A method for encoding and decoding using an AUM block geometric mean labeling is given. Suitable illustrations are also presented.